因式分解~因式分解~因式分解

(x-1)(x-4)(x-2)(x-3)-48
(x2-5x+4)(x2-5x+6)-48
設x2-5x為a
(a+4)(a+6)-48
a2+10a+24-48
a2+10a-24
(a+12)(a-2)
(x2-5x+12)( x2-5x-2)

let a be (x-2)(x-3)=x^2-5x+6
so (x-1)(x-4)=x^2-5x+4=a-2

(x-1)(x-2)(x-3)(x-4)-48
=a(a-2)-48
=a^2-2a-48
=(a-8)(a+6) cross method
=(x^2-5x-2)(x^2-5x+10)